Consistent short range shooting only requires a modest amount of skill and a weapon suitable for firing a reasonably flat and repeatable trajectory out to a couple hundred yards without regard for variations in ambient conditions. To consistently engage targets at long range, however, is a complex function of shooting skill, weapon system quality, reliable data query and, perhaps most importantly, applied math.
Even so, the first thing that a long-range marksman does with his weapon is the same thing that a novice marksman does—he calibrates or “zeroes” it. Typically, a rifle is fitted with a scope via a mounting system such that the scope is rigidly attached to the rifle and positioned in-line with the rifle's barrel. With the scope being rigidly fixed relative to the rifle, adjustments in the scope can be made by manipulating the position of lenses that form the scope.
Though usually not adjustable itself, the mounting system may comprise an inclined base in order to angle the scope's default line of sight (DLOS) slightly downward (default elevation and windage settings of a scope are usually set at the median points within the relative ranges of available adjustment), relative to the baseline represented by the axis of the rifle's barrel bore, so that the DLOS intersects a line projected from the rifle's barrel at a point some distance in front of the rifle. Notably, while an inclined mounting system is not an absolute in all rifle/scope combinations, a marksman would know that it offers potential advantages to a long range marksman including the effective increase of the practical elevation adjustment range of the scope for long distance shots. That is, because the inclined mounting system inherently biases the rifle barrel up relative to the scope's line of sight, the trajectory of the bullet will start off at an upward angle thus necessitating less adjustment for longer shots. Initially, the point of intersection between the DLOS and the barrel axis projection is unknown and of little value to the marksman until the scope is “zeroed” to the rifle such that the point of intersection correlates with a point of bullet impact at a given distance.
When a rifle is zeroed with its scope, the point of a bullet's impact on a target at a given distance will coincide with the DLOS when the bullet is shot at certain ambient conditions and not affected by significant wind or marksman error, i.e. the bullet will hit the target “right on the crosshairs.” Although there is no set standard for selecting a zero distance, zeroing a rifle/scope combination is most often done at a short range, typically 100 yards or less. The reason for short range zeroing is that the trajectory of the bullet is still relatively flat at a short range because the muzzle velocity (the velocity of the bullet at its maximum, i.e. shortly after it exits the barrel) has not degraded to such an extent that gravity has a significant effect on the bullet's flight path. As such, especially with a bullet caliber having a high ballistic coefficient and fast muzzle velocity, variations in ambient conditions, including moderate crosswinds, will not cause enough deviation in the predictable baseline trajectory of the bullet to warrant compensation by a marksman seeking to engage a target at or near the “zero” distance.
For the novice marksman, a properly zeroed rifle means locking down the scope settings and not worrying about the bullet's ballistics whether the shot to be taken is at 25 yards or 150 yards—he knows that the change in trajectory due to the deviation in range off his zero distance is well within the available margin of error for hitting a short range target. For a long range marksman, however, a zero distance serves only as a good, predictable starting point—he's not looking to engage targets at 150 yards but, rather, at significantly longer distances, such as on the order of 1500 yards or more.
The suitability of a given rifle caliber for long range shooting directly correlates with the caliber's ballistic coefficient and muzzle velocity. The higher the ballistic coefficient, the better the particular caliber bullet slices through the atmosphere. The faster the muzzle velocity, the farther the bullet flies before aerodynamic forces reduce the bullet's stability. Therefore, a high ballistic coefficient coupled with a high muzzle velocity is a desirable combination for long range target engagement. However, even calibers with desirable ballistic coefficients and fast muzzle velocities capable of keeping the bullet at supersonic speeds for long distances can drop upwards of 4 feet below DLOS at just 500 yards. At 600 yards, the same exemplary bullet can drop below DLOS an additional 2½ feet. Change the ambient conditions, such as humidity, barometric pressure, temperature and crosswind strength, and that 500 yard shot using the zeroed crosshairs may be 1½ feet to the left of a target and below the DLOS as if it were shot at 600 yards instead of 500.
Clearly, for a long range marksman, the zero distance is just a jumping off point for making adjustments. If long range targets are going to be hit precisely, then factors and conditions such as target distance, crosswind strength, humidity, barometric pressure, coriolis effect, and temperature, among others, must be considered and compensated for. As such, once the rifle has been zeroed at a given distance and ambient conditions, a long range marksman will begin to collect data at varying distances and conditions in order to develop what is known to one of ordinary skill in the art as a Data Observed from Prior Engagements or “DOPE” book.
A DOPE book can be used by the long range marksman to make adjustments in the field based on the actual field conditions for the shot versus the controlled “zero” conditions. More particularly, by referring to the empirical data documented in his DOPE book, a marksman can predict how far off point of impact his DLOS will be and, accordingly, make adjustments to correct the predicted error. However, practicality dictates that a DOPE book can only document so much data and, therefore, it is inevitable that the marksman will often use the DOPE data as a general guide to get him “most of the way home” before applying his judgment and experience to estimate the actual adjustments required to make the shot.
As an example, a given DOPE book may record data for target distances ranging from 500 to 1500 yards in 20 yard increments with a 10 mph crosswind, based on a specific rifle that has been zeroed at 100 yards using a specific round. While the exemplary DOPE book would be useful for the long range marksman seeking to make a shot in the 1000 yard range, it may not be “dead on” as the actual distance to target may have been estimated at 1015 yards with an 8 mph crosswind. To further complicate the calculation, consider that the gun was zeroed at 90% relative humidity and 90 degrees Fahrenheit at sea level, as opposed to the exemplary field conditions being measured at 40% humidity and 30 degrees Fahrenheit on top of a mountain, and one can easily see how drastically different the settings must be from the zero in order to score a hit. The point is that if the marksman doesn't have his “DOPE” book exactly on point, which he rarely does, he must either extrapolate or interpolate the required adjustments.
In addition to the inevitable estimation from DOPE records, the more estimation required on the part of the marksman concerning field conditions, the more likely that the adjustments calculated from those estimations will be inaccurate. Of all the estimations, perhaps the pivotal estimation for a long range marksman is the initial distance to target. Considering that at a 1000 yard distance even a caliber with desirable long range ballistics may be dropping up to one inch for every yard of forward travel, the result of a misjudged distance to target is a significant and costly miss. Underestimate the distance to target by a mere 10 yards and the shot could be almost a foot low.
There are basically two methods used in the art to estimate the all important distance to target. The first method is to “mil” the target and the second method is to use an infrared/laser (IR/Laser) range finding device. IR/Laser ranging devices are very accurate, using the known speed of light bouncing off the target to calculate the distance to target. However, in many applications, such as military sniping, use of an IR/Laser device can be seen by an enemy, thus compromising a sniper's position. For this reason, many long range marksmen rely on the “mil” method.
The process of “milling” a target to determine its distance comprises translating the target's linear height, as seen through an optical viewing device in units of mils, into corresponding units of angular measure which are useful for adjusting a line of sight (e.g., raising the point of aim by pivoting a weapon up). Consequently, if an object's height is known (or accurately estimated), then the number of mils required to demarcate the object's height as seen through an optical viewing device can be used to calculate the distance to the object. With the distance to object calculated and mapped to a known ballistic trajectory curve, adjustments for aim can be given in units of angular measure.
Notably, it will be understood by one of ordinary skill in the art that the use of the term “mil” as a verb, at least as it pertains to estimating target height, distance, crosswind, etc. is a comprehensive term for methods that employ linear and angular units of measure including, but not limited to, mils, minutes of angle, radians, inches per hundred yards and user-defined units. Thus, “milling” is a term in the art and its use is not intended to be limited to methods for calculating ballistic solutions that make use of mils as a unit of measure.
To actually “mil” an object and calculate its distance, an essential device for long range shooting is a scope or range finder that comprises a reticule, i.e. a network of fine lines or markings 15 that can be seen by the marksman when looking through the eyepiece of the scope (FIG. 1A). Range finder devices known in the art, or a scope with a reticule, provide a marksman with a means to determine the distance to target, assuming, of course, that the marksman can accurately estimate the target's height. If the height of the target is known (or accurately estimated), and the distance between the scope or range finder reticule markings can be correlated with an angle of measure, then a right triangle is defined with the target height as the length of the leg opposite the angle of measure. From the defined triangle, the distance to the target can be calculated via the tangent of the determined angle.
Once a target is “milled” based on its estimated or possibly known height, and a distance to target is calculated, a long range marksman can refer to his DOPE card or other ballistic data to determine just how far above the target he needs to aim in order for the bullet to impact the target. Of course, as noted previously, other factors must also be considered. It is well understood to one of ordinary skill in the art that ambient conditions such as barometric pressure, crosswinds, coriolis forces, temperature and humidity directly affect the trajectory of a bullet. Based on the empirical data of the DOPE book or other ballistic data available, the marksman can further amend the elevation calculation to compensate for those factors and arrive at a comprehensive ballistic solution for engaging the target. At such point, an application of the ballistic solution will dictate to the marksman that his particular weapon should be aimed at a certain “mil” height above the target and a certain “mil” distance off center of the target in order to score a hit (thus causing the marksman to adjust the angle at which the rifle is being aimed).
With a ballistic solution identified, the marksman has the option of either 1) leaving the scope at its zero and “holding off” the target as dictated by the ballistic solution or 2) accommodating the ballistic solution by adjusting the elevation and windage settings of his scope. For a marksman applying the first option, the reticule markings used to initially calculate distance can also be used to “hold off” the target according to the ballistic solution. For a marksman applying the second option, a reticule with a plurality of graduated markings within the rifle scope is not required as the mil or MOA angular adjustments will be made to the lenses within the scope, thus “moving” the crosshairs to correspond with the desired point of impact.
Infrared range finding technologies notwithstanding, the calculated distance to a target using trigonometry will only be useful if the marksman can 1) accurately estimate target height and 2) accurately estimate an angle of measure. Accuracy of target height estimation directly correlates with the marksman's ability to make the estimation. Likewise, even though the angle of measure can be determined based on scope or range finder reticule markings, the target may not fit exactly between reticule demarcations and, as such, the angle of measure estimation is also a function of marksman skill.
Therefore, to improve the accuracy of distance to target estimations for long range marksmen, there is a need in the art for devices and methods that can improve the estimation of inputs used to calculate target distance and/or target height. Further, there is a need in the art to improve the accuracy of ballistic solutions via devices and methods used to collect and manipulate data that affects bullet flight.